Discount Nominal Cash Flows at the Nominal Risk-Free Rate

Summary

The document considers whether to discount nominal cash flows using expected inflation or the nominal risk-free rate when inflation is higher. It argues for the nominal risk-free rate, using a one-year zero-coupon bond as a no-arbitrage example. Discounting a nominal payoff at a rate above the risk-free rate would make the bond appear cheaper than the cost of funding its purchase, allowing a riskless profit in the stated setup.

The conclusion is that nominal cash flows should be discounted consistently with the nominal risk-free rate to avoid that arbitrage. Inflation is relevant to converting between nominal and real quantities, but the example does not develop real cash-flow valuation, risky discount rates, or term structures. Its illustration uses a simplified single-period setting and approximate values; actual valuation requires rates and cash flows matched by currency, maturity, and nominal or real basis.

Key ideas

• The example frames discount-rate choice as a no-arbitrage valuation problem.
• Discounting a nominal payoff above the nominal risk-free rate can create a funding arbitrage in the stated setup.
• Nominal cash flows should be paired with nominal discount rates.
• The illustration is a simplified one-period example and does not address risky cash flows or real valuations.

Tags

# Valuation discount rate using risk free interest rate versus inflation rate


# Valuation discount rate using risk free interest rate versus inflation rate












Imagine a world where, for a given time period, the expected inflation rate is 10%, but the nominal risk free interest rate over the same period is 5%.

Should my starting point - from a discounted valuation perspective - use 10% or 5% as the discount rate?

All in nominal terms.

## Answer by mmencke (score 1)

https://quant.stackexchange.com/a/69369

To avoid arbitrage opportunities in your valuation model, you have to use the nominal risk-free interest rate as a discount rate:

Let us consider a Zero Coupon Bond (ZCB) expiring in one year with a (nominal) payoff of 1. If we discount with 10% then this ZCB would cost approximately 0.9.

Let us assume that we buy the ZCB for 0.9 using money borrowed in the bank at the risk-free rate of 5%. This would be an initially costless strategy. After one year we would have to pay the loan back and this would cost us approximately 0.95. We receive 1 from the ZCB meaning that we can pocket approximately 0.05 by putting up no money and taking no risk. This is thus an arbitrage opportunity. To avoid arbitrage opportunities in the model we must use a the nominal risk-free rate to value nominal cash flows.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.